Question 457412
How long will it take $750 to be worth $1000 if it is invested at 5% interest compounded quarterly?
.
A = P(1 + r/n)^(nt)
where 
A is amount after time t (1000)
P is the principal (750)
r is the rate (.05)
n is the times compounded (4)
t is time (what we're solving for)
.
A = P(1 + r/n)^(nt)
{{{1000 = 750(1 + .05/4)^(4t)}}}
{{{1000 = 750(1.0125)^(4t)}}}
{{{1.3333 = (1.0125)^(4t)}}}
{{{log(1.0125,1.3333) = 4t}}}
{{{log(1.3333)/log(1.0125) = 4t}}}
{{{log(1.3333)/(4*log(1.0125)) = t}}}
{{{5.8 = t}}}
.
that is,
t = 5.8 years